The equation

$$2^{333 x-2}+2^{111 x+2}=2^{222 x+1}+1$$

has three real roots. Given that their sum is m / n, where m and n are relatively prime positive integers, find m+n.

The equation

$$2^{333 x-2}+2^{111 x+2}=2^{222 x+1}+1$$

has three real roots. Given that their sum is m / n, where m and n are relatively prime positive integers, find m+n.