AMC 12B 2013 Problem 22

Let m>1 and n>1 be integers. Suppose that the product of the solutions for x of the equation

8\left(\log _{n} x\right)\left(\log _{m} x\right)-7 \log _{n} x-6 \log _{m} x-2013=0

is the smallest possible integer. What is m+n ?

Answer Choices
A. 12
B. 20
C. 24
D. 48
E. 272