(12) The sum of all real roots of the equation $\left|x^{2}-3 x+2\right|+\left|x^{2}+2 x-3\right|=11$ is $\qquad$ .
(12) The original equation can be transformed into $|x-1|(|x-2|+|x+3|)=11$.

When $x \leqslant-3$, the equation becomes $2 x^{2}-x-12=0$, both roots of which are greater than -3, so there is no solution at this time;

When $-3<x \leqslant 1$, the equation becomes $-2x + 4 = 11$, which has no solution;

When $1<x \leqslant 2$, the equation becomes $-2x + 4 = 11$, which has no solution;

When $x>2$, the equation becomes $2 x^{2}-x-12=0$, one of its roots $x=$ $\frac{1+\sqrt{97}}{4}$ satisfies the condition.

In summary, the sum of all real roots of the equation is $-\frac{6}{5}+\frac{1+\sqrt{97}}{4}=$ $\frac{-19+5 \sqrt{97}}{20}$. Therefore, the answer is $\frac{-19+5 \sqrt{97}}{20}$.