For the system of linear equations in $x , y$:
$$\left( \begin{array} { l l }
5 & a \\
a & 3
\end{array} \right) \binom { x } { y } = \binom { x + 5 y } { 6 x + y }$$
Find the sum of all real values of $a$ such that the system has a solution other than $x = 0 , y = 0$. [4 points]