Calculus Level 2

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

If the definite integral above can be expressed as $$a \sqrt b$$ where $$a,b$$ are positive integers with $$b$$ square free, then what is the value of $$ab$$?

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