Consecutive Odd Integers

Algebra Level 2

The difference of the cubes of two consecutive odd positive integers is 400 more than the sum of their squares. Find the sum of the two integers.

Clarification: The odd positive integers are $1, 3, 5, 7, 9, \ldots.$ Two consecutive odd positive integers refer to two consecutive numbers in this sequence. It does not refer to two consecutive integers (of which one will not be odd).

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