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Let $x$ and $y$ be positive numbers such that $\begin{cases} x^2+y\sqrt{xy}=2013, \\ y^2+x\sqrt{xy}=671. \\ \end{cases}$

If $y^2 = \frac{a}{b}$ where $a$ and $b$ are positive coprime numbers, what is $a+b$?

This problem is posed by Samir K.

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