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Let \(\alpha\) and \(\beta\) be the roots of \( 3 x^{2} + 4x + 9 = 0\). Then \( (1+ \alpha)(1 + \beta)\) can be expressed in the form \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers. Find \(a+b\).

This problem is posed by Ron G.

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