a, $\left(2x+3\right)^2=\dfrac{9}{121}\Rightarrow\left(2x+3\right)^2=\left(\sqrt{\dfrac{9}{121}}\right)^2$

$\Rightarrow2x+3=\sqrt{\dfrac{9}{121}}=\pm\dfrac{3}{11}$

$\Rightarrow\left[{}\begin{matrix}2x+3=\dfrac{3}{11}\\2x+3=\dfrac{-3}{11}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{\left(\dfrac{3}{11}-3\right)}{2}\\x=\dfrac{\left(\dfrac{-3}{11}-3\right)}{2}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{-15}{11}\\x=\dfrac{-18}{11}\end{matrix}\right.$

b, $\left(3x-1\right)^3=\dfrac{-8}{27}$

$\Rightarrow\left(3x-1\right)^3=\dfrac{-8}{27}\Rightarrow\left(3x-1\right)^3=\left(\dfrac{-2}{3}\right)^3$

$\Rightarrow3x-1=\dfrac{-2}{3}\Rightarrow3x=\dfrac{1}{3}\Rightarrow x=\dfrac{1}{9}$