The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.1225\\[1 em]x_2 &= -1.1225\\[1 em]x_3 &= 0.5612+0.9721i\\[1 em]x_4 &= 0.5612-0.9721i\\[1 em]x_5 &= -0.5612+0.9721i\\[1 em]x_6 &= -0.5612-0.9721i \end{aligned} $$Polynomial $ x^6-2 $ has no rational roots that can be found using Rational Root Test, so the roots were found using Newton method.