Bi-Quadratic Equation

The given equation can be written as:-

$(x^2-4x+1)(x^2+x+1)=0$

Roots of $x^2-4x+1=0$ are $2+\sqrt{3}$ and $2-\sqrt{3}$

Roots of $x^2+x+1=0$ are $\omega$ and $\omega^2$ where $\omega$ is complex cube root of unity

$|\omega|=|\omega^2|=1$

$\Rightarrow$ Sum of Moduli of roots are:- $(2+\sqrt{3})+(2-\sqrt{3})+1+1=\boxed{6}$