Logarithm and a special ratio

Algebra Level 4

$\large \log_{32}{x}=\log_{\sqrt{2016}}{y}=\log_{63}{(x+y)}$

If $$x$$ and $$y$$ are real numbers and $$\dfrac{y}{x}$$ is of the form $$\dfrac{a+\sqrt{b}}{c}$$, where $$a,b$$ and $$c$$ are integers such that $$b$$ is square-free, find $$a+b+c$$.

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