Samir's system of equations

Algebra Level 4

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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