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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