An interesting equation

Algebra Level 4

The equation \(x^3+12x^2-x-7=0\) has three real roots. Now, the equation \(ay^3+by^2-cy+d=0\) has the roots of the previous equation increased by \(4\), where \(\text{gcd}(a,b,c,d)=1\). Find \(a+b+c+d\)

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