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Calculus Level pending

For the equation \(x^2+2xy+2y^2+2x+2y+1 = 0 \), we are given that \( \dfrac{d^2 y}{dx^2} = \dfrac{abc+2fgh-af^2-bg^2-ch^2}{(hx+by+f)^3} \), where \(a,b,c,f,g\) and \(h\) are constants.

Find \(a+b+c+f+g+h\).

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