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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