AMC 12 2013b Problem 22

Let $m>1$ and $n>1$ be integers. Suppose that the product of the solutions for $x$ of the equation $$8(\log_n x)(\log_m x)-7\log_n x-6 \log_m x-2013 = 0$$ is the smallest possible integer. What is $m+n$?

\textbf{(A)}\ 12 \textbf{(B)}\ 20 \textbf{(C)}\ 24 \textbf{(D)}\ 48 \textbf{(E)}\ 272