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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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