If $[x]^2-5[x]+6=0$, where [.] denotes the greatest integer function, then

Let $\mathrm{f}: \mathbb{R}-\{2\} \rightarrow \mathbb{R}-\{1\}$ defined by $\mathrm{f}(x)=\frac{x-3}{x-2}$ and $\mathrm{g}: \mathbb{R} \rightarrow \mathbb{R}$ defined by $\mathrm{g}(x)=3 x-2$, then sum of all values of $x$ for which $\mathrm{f}^{-1}(x)+\mathrm{g}^{-1}(x)=\frac{19}{6}$ is

$$ \begin{aligned} & f(x)=\left\{\begin{array}{ll} 3-x, & -1 \leqslant x<0 \\ 1+\frac{5 x}{3}, & -3 \leqslant x \leqslant 2 \end{array}\right. \text { and } \\ & g(x)=\left\{\begin{aligned} -x, & -2 \leqslant x \leqslant 3 \\ x, & 0 \leqslant x \leqslant 1 \end{aligned}\right. \end{aligned} $$

then range of (fog) $(x)$ is