Let line \({\bf L}\) be the tangent line to the curves \({\bf f(x) = -x^2 }\) and \( {\bf g(x) = \sqrt{x}. }\)

The area bounded by line \({\bf L }\) and the two curves \( {\bf f(x) = -x^2 }\) and \( {\bf g(x) = \sqrt{x} }\) can be represented as \({\bf \frac{m}{n}, } \) where \({\bf m }\) and \({\bf n }\) are coprime positive integers.

Find \({\bf m + n .}\)

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