Rooted away

Algebra Level 4

\(x\) is a real number that satisfies the equation

\[ x = \sqrt{4-x}\sqrt{5-x} + \sqrt{5-x}\sqrt{6-x} + \sqrt{6-x}\sqrt{4-x}. \]

If \(x\) can be expressed as \( \frac{a}{b} \), where \(a\) and \(b\) are coprime positive integers, what is \(a+b\)?

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