\[(x+17)^2+(2x+16)^2+(3x+15)^2+\ldots+(16x+2)^2+(17x+1)^2=0\]

If \(\alpha \) and \(\beta\) are the roots of the equation above, and suppose \(| \alpha + \beta - \alpha \beta | = \frac a b\) for coprime positive integers \(a,b\), find the value of \(a+b\).

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