\(\left|x+\dfrac{1}{3}\right|-4=-1\)

\(\Rightarrow\left|x+\dfrac{1}{3}\right|=3\)

\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{1}{3}=3\\x+\dfrac{1}{3}=-3\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{8}{3}\\x=-\dfrac{10}{3}\end{matrix}\right.\)