Radical Integral Of Radicals

Calculus Level 3

\[ \int_3^6 \left ( \sqrt{x + \sqrt{12x-36}} + \sqrt{x - \sqrt{12x-36}} \ \right ) \ dx \]

If the definite integral above can be expressed as \(a \sqrt b\) where \(a,b\) are positive integers with \(b\) square free. What is the value of \(ab\)?

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