Is the answer complex?

Calculus Level 2

Let \(y = \sqrt{x+\sqrt{12x-36}}\).

The value of \(\dfrac{dy}{dx}\) at \(x = 4\) can be expressed as \(\dfrac{m}{n}\) , where \(m , n \) are co-prime positive integers.

Find the value of \(m+n\)

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