Easy Peasy..!!

Algebra Level 3

\[ \large \log_{\sqrt[2]{3}} (x+y) = 2 , \log_{\sqrt[3]{5}} (x-y) = -3 \]

The system of equation above holds true for real numbers \(x\) and \(y\). If \(2x+5y\) can be written as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a-b\).

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