Transformation of Roots!

Algebra Level 4

P(x)=x33x+1\Large{P(x) = x^3 - 3x+1}

Let Q(x)=x3+Ax2+Bx+CQ(x) = x^3 + Ax^2 + Bx + C be a polynomial with integer coefficients such that its roots are the fifth powers of the roots of P(x)P(x). Evaluate A+B+CA+B+C.

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