You are misunderstanding how levels work in general. When you gain a level, you put it into a class and become level X+1 in that class. Each class functions completely independently of each other except for specific abilities that say they stack with other classes.
In your example, when you add a new level to Duskblade, you become an Duskblade 6/Abjurant Champion 5. Now, Abjurant Champion does not "add to" Duskblade levels. It only has this statement under its Spellcasting ability.
At each level, you gain new spells per day
and an increase in caster level (and spells known, if applicable)
as if you had also gained a level in an arcane spellcasting class
to which you belonged before adding the prestige class level.
You do not, however, gain any other benefit a character of that
class would have gained. If you had more than one arcane
spellcasting class before becoming an abjurant champion, you
must decide to which class to add each level for the purpose of
determining spells per day, caster level, and spells known.
So the Abjurant Champion levels add to your Duskblade caster levels allowing you to cast as an 11th level caster (and the other benefits listed) - but that's it, nothing else, certainly not the same as being a Duskblade 11. See Class level vs. Character level vs. "my" level for more of an explanation of class level vs character level vs spellcasting level.