The sum of the roots of the equation $2^{33x-2}+2^{11x+2}=2^{22x+1}+1$ is

Let $2^{11x}=t$,  given  equation reduces to $\frac{t^3}{4}+4t=2t^2+1$

$\begin{array}{l}\Rightarrow t^3-8t^2+16t-4=0\Rightarrow t_1\cdot t_2\cdot t_3=4\\ \Rightarrow 2^{11x_1}\cdot 2^{11x_2}\cdot 2^{11x_3}=4\Rightarrow 2^{11\left(x_1+x_2+x_3\right)}=2^2\\ \Rightarrow 11\left(x_1+x_2+x_3\right)=2\\ \therefore x_1+x_2+x_3=\frac{2}{11}\end{array}$