The common value of the 6th  roots of unity and cube roots of unity are ____________

$\mathrm{cube} \mathrm{roots} \mathrm{of} \mathrm{unity} \mathrm{are} 1,\mathrm{\omega },{\mathrm{\omega }}^2$

$x^6=1\Rightarrow x^2=1,\omega ,{\omega }^2$

$6\mathrm{th} \mathrm{roots} \mathrm{of} \mathrm{unity} \mathrm{are} \pm 1,\pm \mathrm{\omega },\pm {\mathrm{\omega }}^2$

$x^6-1=\left(x^3-1\right)\left(x^3+1\right)$

Therefore common roots of 6th roots and cube roots of unity are $1,\mathrm{\omega },{\mathrm{\omega }}^2$ (i.e) $1,\frac{-1+\mathrm{i}\sqrt{3}}{2},1,\frac{-1-\mathrm{i}\sqrt{3}}{2},$