(Almost) degree 6 equation

Algebra Level 4

If α,β\alpha, \beta are the real roots of the equation (x2+9)3+216x3=(x+3)6(x^{2}+9)^{3} + 216x^{3} = (x+3)^{6}.

Find the value of α6+β6\alpha^{6} + \beta^{6}.

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