The answer to this is not fully clear in the rules as written, as "Resist All" is not clearly defined anywhere; the DM must interpret this rare and unlikely edge case as they see fit.
A rules-as-written answer to this question requires a clear definition of "Resist 1 All". Unfortunately, that term is not clearly defined anywhere in the rules. This answer to another question on Resist All covers this problem well.
The general definition of Resist is clear. As per Rules Compendium p.224:
Resistance means a creature takes less damage from a specific damage type.
But an item which grants Resist All contradicts this definition. Yes, Resist 5 Fire unambiguously reduces all fire damage by 5, but does Resist 5 All reduce all damage, or all damage types? The general rule on Resist does not help us to understand Resist All.
Therefore, in this ambiguous, rare and unlikely case (involving a specific power against a specific armor and quibbling over one point of damage), the rules-as-written just don't give us enough information, and the DM must interpret the rules and make their own ruling on this case.
Interpretation 1: Resist all damage
If you resist all damage, then you simply take less damage every time you take damage, regardless of type. References to "resist all damage" appear throughout the rules. Rules Compendium p.225:
Similarly, if a creature has resist 5 cold and then gains resist 2 to all damage, the creature still has resist 5 cold, not resist 7 cold.
The creature has resist 20 to all damage.
From these examples we definitively know that one can have resistance to "all damage", despite the general rule on the Resist property saying that it only stops one specific named type. In order to resist all damage, you must, by definition, also resist untyped weapon damage, which is explicitly not a type according to Rules Compendium p. 223:
If the power doesn't specify a damage type, the damage has no type. Most weapon attack powers deal damage that has no type.
Interpretation 2: Resist all types
However, there is no equivalent precedent that unambiguously shows someone being resistant to all elements (but not untyped weapon damage). Despite the general rule that Resist only hinders types, there are clear precedents that show Resist applying to all damage. The only argument here is to interpret "Resist 1 All" as "Resist 1 All Types", which, although the DM may rule it, is not strongly supported by existing rules.
One or two damage?
Under the "resist all damage" interpretation, the most likely ruling is that it resists 1 damage. Rules Compendium p.222:
When a typical attack hits a target, the attack deals damage to it, reducing the target's hit points. Each attack specifies how much damage it deals, if any ... Damage is almost always instantaneous.
And, as specified above, resistance triggers whenever you take damage. Yes, it says "from a specific damage type", but under the principle of specific overrides general, Resist All resists all damage, not a specific type. It therefore does not trigger each time you take a different element, but each time you take any damage.
The "resist all types" interpretation, however, forces us to ask whether standard resistance triggers per damage, or per type. The rule as above says that it triggers when you take damage from that type. It seems to me that when you take damage of two types which you resist, resistance should apply to both; there is no explicit limit of one resistance. (This would be different of course if you took, say, "5 fire and cold", a combined damage type; but here you are taking x fire and x cold, and while you take only one chunk of instantaneous damage, resistance triggers whenever you take that type of damage, and you took two types.)
Hence, under a "resist all types" interpretation, you would likely resist 2 damage, though of course this is already highly up to DM's interpretation.
There is no clear rules-as-written answer in this case, which is why most answers to this question fall back to rules as intended or community interpretation.
The meaning of Resist 1 All is ambiguous and could mean either Resist 1 All Types or Resist 1 All Damage, but there are several precedents for Resist All Damage and none for Resist All Types.
The most likely interpretation to this ambiguous situation requiring DM adjudication is therefore that you resist all damage, and only resist 1 damage per attack regardless of type.