number theory for finding value of $k$ How do I find what is the smallest positive integer $k$ such that $(3^3 + 4^3 + 5^3)\cdot k = a^n$ for some positive integers $a$ and $n$, with $n > 1$?

$(3^3 + 4^3 + 5^3)\cdot k =6^3k= a^n $ in which is obvious that $(k,n,a)=(1,3,6)$
