Respective values

$\begin{aligned} \frac {5x-11}{2x^2+x-6} & = \frac {5x-11}{(x+2)(2x-3)} \\ \implies \frac G{x+2} + \frac W{2x-3} & = \frac {5x-11}{(x+2)(2x-3)} & \small \color{#3D99F6} \text{Multiplying both sides by }x+2 \\ G + \frac {W(x+2)}{2x-3} & = \frac {5x-11}{2x-3} & \small \color{#3D99F6} \text{Putting }x=-2 \\ \implies G & = \frac {5(-2)-11}{2(-2)-3} = 3 & \small \color{#3D99F6} \text{Similarly }\times (2x-3) \text{ and }x=\frac 32 \\ \implies W & = \frac {5\left(\frac 32\right)-11}{\left(\frac 32\right)+2} = -1 \end{aligned}$

$\implies \boxed{G = 3, \ W = -1}$

$\dfrac{5x - 11}{2x^2 + x - 6}=\dfrac{G}{(x + 2)}+\dfrac{W}{2x - 3}$

$\dfrac{5x - 11}{2x^2 + x - 6}=\dfrac{G(2x-3)+W(x+2)}{2x^2 + x - 6}$

$G(2x-3)+W(x+2)=5x - 11$

This is equivalent to a system of equations for G and W

$2G+W=5$

$3G+2W=11$

Solution is $\boxed{G=3, W=-1}$