1999 AHSME 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 \qquad \mathrm{(B) \ } 3\qquad \mathrm{(C) \ } 33\qquad \mathrm{(D) \ }35 \qquad \mathrm{(E) \ } 99

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.