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Algebra Level 3

If $$a + b = 1$$ and $$a^2 + b^2 = 2$$, with $$a > b$$, then

$\frac{ a^3 + b^3 }{ a^3 - b^3 } =\frac{ m \sqrt 3 }{ n }$

where $$m$$ and $$n$$ are positive coprime integers, find $$m + n$$.

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