High school math questions, algebra.

the difference between a positive integer, n, and its cube is 4896. Compute n.
Please give solution and detailed explanation! Thank you ver much!
I tried and got 17, but what i did is to try numbers one by one, so i would really appreciate if anyone can tell me the right and systematic way to tackle this question??

Answer

$\textbf{HINT-}$ you have to solve $n^3-n-4896=0$. $n=17$ is the only real solution to this cubic. So there are none other.