$\frac {2x - 4 \sqrt 2}{2 \sqrt{x^2 - 4 \sqrt 2 x + 16} } + \frac {2x - 3 \sqrt 2}{2 \sqrt{x^2 - 3\sqrt 2 x + 9} } = 0$

If the real value of $\large{x}$ which satisfies the equation above can be expressed as $\frac { a\sqrt { b } }{ c }$, find $a+b+c$.

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