2013 Fermat Problem 19

There are two ways of choosing six different numbers from the list 1, 2, 3, 4, 5, 6, 7, 8, 9 so that the product of the six numbers is a perfect square. Suppose that these two perfect squares are m^2 and n^2, with m and n positive integers and m \neq n. What is the value of m + n?

\textbf{(A)}\ 108\quad \textbf{(B)}\ 11\quad \textbf{(C)}\ 61\quad \textbf{(D)}\ 56\quad \textbf{(E)}\ 144

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Full credit to this problem is given to the CEMC, you may view all Fermat contests here.