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If α,β\alpha, \betaα,β are the real roots of the equation (x2+9)3+216x3=(x+3)6(x^{2}+9)^{3} + 216x^{3} = (x+3)^{6}(x2+9)3+216x3=(x+3)6.
Find the value of α6+β6\alpha^{6} + \beta^{6}α6+β6.
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