Algebra Level 4

$\displaystyle \sqrt{ y - \sqrt{ y - \sqrt{ y - \cdots }}} = \sqrt{ x + \sqrt{ x + \sqrt{ x + \cdots }}}$

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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