2007 AMC 10A Problem 17

Suppose that m and n are positive integers such that 75m = n^{3}. What is the minimum possible value of m + n?

\text{(A)}\ 15 \qquad \text{(B)}\ 30 \qquad \text{(C)}\ 50 \qquad \text{(D)}\ 60 \qquad \text{(E)}\ 5700

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