# A Sum of Roots of Roots

Algebra Level 3

The real number $$x$$ satisfying the equation $\sqrt{ x + \sqrt{2x-1} } + \sqrt{x - \sqrt{2x-1} } = 10$ can be written as $$\frac{a}{b}$$ where $$a$$ and $$b$$ are positive coprime integers. Find $$a+b$$.

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