A Sum of Roots of Roots

Algebra Level 3

The real number xx satisfying the equation x+2x1+x2x1=10 \sqrt{ x + \sqrt{2x-1} } + \sqrt{x - \sqrt{2x-1} } = 10 can be written as ab \frac{a}{b} where aa and bb are positive coprime integers. Find a+ba+b.

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