Rooted away

Algebra Level 4

xx is a real number that satisfies the equation

x=4x5x+5x6x+6x4x. x = \sqrt{4-x}\sqrt{5-x} + \sqrt{5-x}\sqrt{6-x} + \sqrt{6-x}\sqrt{4-x}.

If xx can be expressed as ab \frac{a}{b} , where aa and bb are coprime positive integers, what is a+ba+b?

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