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

Let,  $t=2^{11x}$

$\Rightarrow \frac{{\left(2^{11x}\right)}^3}{2^2}+2^{11x}{.2}^2={\left(2^{11x}\right)}^2.2+1$

$\frac{t^3}{4}+4t=2t^2+1$

$\Rightarrow t^3-8t^2+16t-4=0$

Cubic it t has roots $t_1,t_2,t_3$

$t_1{t}_2{t}_3=4\Rightarrow 2^{11x_1}{.2}^{11x_2}{.2}^{11x_3}=4$

$\Rightarrow 2^{11(x_1+x_2+x_3)}=2^2$

$\Rightarrow 11(x_1+x_2+x_3)=2\Rightarrow x_1+x_2+x_3=\frac{2}{11}$