\[\displaystyle \sqrt{ y - \sqrt{ y - \sqrt{ y - \cdots }}} = \sqrt{ x + \sqrt{ x + \sqrt{ x + \cdots }}} \]

Given the equation above, it is found that \(x\) and \(y\) are related as \(\displaystyle \frac{y-x+1}{y-x -1} = \frac{\sqrt{1 + ay}}{\sqrt{1 + bx}} \) for some positive integers \(a\) and \(b\).

Evaluate: \(a+b\)

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