The Play of Roots

Level pending

\(x^3 +4x -1 = 0\) has roots \( \alpha , \beta, \gamma\) and \(6y^3 -7y^2+ 3y -1 =0\) where \( y= \frac {1}{1+x}\). If \[ \frac {(\beta+1)(\gamma+1)}{(\alpha+1)^2} + \frac {(\gamma+1)(\alpha+1)}{(\beta+1)^2} + \frac {(\alpha+1)(\beta+1)}{(\gamma+1)^2}\] can be expressed as \(\frac {a}{b}\) where a and b are coprime integers, find \(a+b\).

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