I am stumped on this one.

Assume m and n are positive integers. 75m = n^3. What is the minimum possible value of m + n?

a) 15

b) 30

c) 50

d) 60

e) 5700

I was unsure of where to begin, so I tried to set up a system of equations and try each possible answer.

75m = n^3, m + n = 15

But, this gave me imaginary numbers when I tried solving each possible answer. I'm guessing that I'm going at this completely wrong.

I know that when you have a quadratic you can find the minimum by -b/2a when in the form y = ax^2 + bx + c, but I didn't think I could do this when I have a cube there.