\[ \large (x^2+5x+6)^{2x^2-x-1} = 1 \]

Given that \(Ax^2 + Bx + C = 0 \) is a quadratic equation whose two roots (of \(x\)) are the reciprocal of the values of \(x\) that satisfy the exponential equation above. And if the greatest common divisor of \(A,B,C\) equals to 1, find the value of \(A+B+C \).

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