No, but you can cast it on the 10' cubic box the pole fits in
This is an interesting puzzle you present. It is clear, as you say, that an 11 foot pole is not a legitimate target for a light spell. And yet, you assume, a 10 x 10 x 10 box is a legitimate target for the spell. Since the pole will clearly fit inside the box, in some sense the box is larger. How can the larger box not be too big while the smaller pole is too big?
Like Light, a number of spells in the PHB target objects of limited size: Drawmij's Instant Summons ("an object weighing 10 pounds or less whose longest dimension is 6 feet or less"), Mending (a "break or tear [that] is no larger than 1 foot in any dimension"), Nondetection ("a willing creature or a place or an object no larger than 10 feet in any dimension"), Stone shape ("a stone object of Medium size or smaller or a section of stone no more than 5 feet in any dimension"), and Wish (an "object [of] no more than 300 feet in any dimension").
Referencing these descriptions themselves only, it is not clear what "any dimension" means. A number of commenters (on other answers and earlier versions of this answer) have pointed out that "any dimension" can include the 'space diagonal' of a three dimensional object, which is longer than any of its sides. For example, a 10' x 10' x 10' box has a face diagonal of over 14 feet on each surface and a space diagonal of over 17 feet running through its interior. Thus, they reason that a 10' cube is not a legitimate target for a light spell, since it has an interior dimension of nearly double ten feet.
However, two sections of the PHB make it clear "how dimensions are supposed to work": dimension does NOT include diagonals.
Move Earth says
Choose an area of terrain no larger than 40 feet on a side within range. You can reshape dirt, sand, or clay in the area in any manner you choose for the duration. You can raise or lower the area’s elevation, create or fill
in a trench, erect or flatten a wall, or form a pillar. The extent of any such changes can’t exceed half the area’s largest dimension. So, if you affect a 40-foot square, you can create a pillar up to 20 feet high, raise or lower the square’s elevation by up to 20 feet, dig a trench up
to 20 feet deep, and so on.
If the "area's largest dimension" were allowed to be the diagonal, you could lower the elevation by more than 28 feet. By stating that the maximum change is 20 feet, the spell is clearly indicating that only the "sides" (and not the diagonal) count as its largest dimension.
The Monk Disciple of the Elements Class Feature Shape the Flowing River says
As an action, you can spend 1 ki point to choose an area of ice or water no
larger than 30 feet on a side within 120 feet of you. You can change water to ice within the area and vice versa, and you can reshape ice in the area in any manner you choose. You can raise or lower the ice’s elevation, create
or fill in a trench, erect or flatten a wall, or form a pillar. The extent of any such changes can’t exceed half the area’s largest dimension. For example, if you affect a 30-foot square, you can create a pillar up to 15 feet high, raise or lower the square’s elevation by up to 15 feet, dig
a trench up to 15 feet deep, and so on. You can’t shape the ice to trap or injure a creature in the area.
As with move earth, the description of this ability makes it clear that the "largest dimension" can be either length or width measured along the surface, but not an interior diagonal.
Thus, an 11 foot pole is not a valid target of the light spell because its largest dimension, its length, is longer than 10 feet. However, such a pole can easily fit within a 10' x 10' x 10' box. By choosing the dimensions of face diagonals and space diagonals, it is clear that some dimensions of the box are larger than 10 feet. However, according to the way the PHB indicates that dimensions work, these diagonal dimensions do not count for the application of the size limit of the spell, merely its exterior length, width, and height.
