AHSME 1999 Problem 30

The number of ordered pairs of integers $(m,n)$ for which $mn \ge 0$ and

$m^3 + n^3 + 99mn = 33^3$ is equal to $\mathrm{(A) \ }2 \mathrm{(B) \ } 3 \mathrm{(C) \ } 33 \mathrm{(D) \ }35 \mathrm{(E) \ } 99$