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$x$ 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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