\(x\) 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 \(a+b\)?
by
Calvin Lin
