Can you find a four digit number N that can be divided by 11, with the sum of the cubes of its digits is equal to N/11?
For example, 1342 / 11 = 122, but 1^3 + 3^3 + 4^3 + 2^3 = 1 + 27 + 64 + 8 = 100, which does not equal 122.
The problem is inspired by an old math olympiad question.
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