# Cubic Diophantine

Number Theory Level 3

If $$x$$ and $$y$$ are positive rational numbers that satisfy the equation $$x^{3}+y^{3}+\dfrac{1}{27}=xy$$, the value of $$x+y$$ can be expressed in the form $$\dfrac{m}{n}$$. Where $$m$$ and $$n$$ are coprime positive integers, find $$m+n$$.

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