AHSME 1979 Problem 22

Find the number of pairs $(m, n)$ of integers which satisfy the equation $m^3 + 6m^2 + 5m = 27n^3 + 27n^2 + 9n + 1$. $\textbf{(A) }0 \textbf{(B) }1 \textbf{(C) }3 \textbf{(D) }9 \textbf{(E) }\infty$