\(x\) satisfies the equation \[\sqrt{x+\sqrt{x}}-\sqrt{x-\sqrt{x}}=\dfrac{199}{100}\sqrt{\dfrac{x}{x+\sqrt{x}}}\]

Also, its value can be expressed in the form \(\frac{m}{n}\), where \(m\) and \(n\) are coprime positive integers, find \(m+n\).

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