What A Lucky Coincidence

Level pending

The area, in the Cartesian plane, between the two parabolas \(\alpha\) (\(y + \frac{a}{b} = x^2\)) and \(\beta\) (\(y + x^2 = \frac{a}{b}\)) is \(\frac{a}{b}\), for positive integer coprime values of \(a\) and \(b\).

Evaluate \(a+b\).

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