(Note: I do not disagree with the other answers already given. However, what I think they miss is that the OP is thinking specifically about a physical box, rather than a cube in space. A cube in space is a common area of effect for a spell, but I would like to more directly address the OP’s thoughts about the significance of literally putting things inside other things)
No, because objects are solid
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?
First we have to clarify that a 10′ x 10′ x 10′ box is not a legitimate target for the light spell. Each of the 10 x 10 panels on the five or six faces of the box has a diagonal of over 14 feet. They are each larger than ten feet “in any dimension” and thus the spell will not work on such a box. However, this does not invalidate your question.
Suppose instead that we have a box of about 7′ x 7′ x 7′. The diagonals of the faces are now under 10 feet and thus the box itself can have light cast upon it. However, the “space diagonal” (not along the faces but from opposite corners in three dimensions) of such a seven-foot box is over 12 feet. Note that the 11 foot pole cannot be lain flat in the bottom of the box, but it will easily fit inside along the space diagonal. Thus, we are back to your original question, why can light be cast on the larger box but not the smaller pole?
To resolve this, it is necessary to understand that in 5e, objects are solid.
Objects (emphasis mine):
When characters need to saw through ropes, shatter a window, or smash a vampire’s coffin, the only hard and fast rule is this: given enough time and the right tools, characters can destroy any destructible object.
Use common sense when determining a character’s success at damaging an object. Can a fighter cut through a section of a stone wall with a sword? No, the sword is likely to break before the wall does.
For the purpose of these rules, an object is a discrete, inanimate item like a window, door, sword, book, table, chair, or stone, not a building or a vehicle that is composed of many other objects.
While it is not stated explicitly, the emphasis on objects being both discrete and breakable makes it clear that the rules consider objects to be solids, not liquids or gasses.
Thus a 7′ x 7′ x 7′ box is a legitimate target of a sleep spell because any of its solid dimensions is less than 10 feet. It does have a 12 foot space diagonal, but since this is composed of empty air, that doesn’t count as part of the object. This is why your 11 foot pole, on which you cannot cast light, can easily fit inside the 7 foot box, on which you can cast light.