Absolute Value Equations #2

Algebra Level 4

Given that the sum of all possible values of $x$ that satisfy the equation

$\large |3x-2|-|x+1|=x+2$

can be expressed in the form $\dfrac{m}{n}$ , where $m$ and $n$ are coprime positive integers, find the value of $m+n$ .

This problem is part of the set Absolute Value Equations.