# X, Y, Dead?

**Number Theory**Level 5

Call an ordered pair of positive integers \( (x, y) \) *dead* if \( (x-y)(x^2+xy+y^2)-xy=61 \). Find the sum of all \( x+y \) over all dead pairs of positive integers.

If you think there are no pairs of dead integers, enter 0. If you think there are infinitely many pairs of dead integers, enter 1000.

**Clarifications**: If you think there are 2 pairs of dead integers, (1, 2) and (3, 4), your answer would be \( (1+2)+(3+4)=10 \).