\(2cos\left(x+\dfrac{\pi}{6}\right)-1=0\Rightarrow cos\left(x+\dfrac{\pi}{6}\right)=\dfrac{1}{2}\)
\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{\pi}{6}=\dfrac{\pi}{3}+k2\pi\\x+\dfrac{\pi}{6}=-\dfrac{\pi}{3}+n2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{6}+k2\pi\\x=-\dfrac{\pi}{2}+n2\pi\end{matrix}\right.\)
\(\left\{{}\begin{matrix}-\dfrac{\pi}{2}\le\dfrac{\pi}{6}+k2\pi< 2\pi\\-\dfrac{\pi}{2}\le-\dfrac{\pi}{2}+n2\pi< 2\pi\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}-\dfrac{1}{3}\le k< \dfrac{11}{12}\\0\le n< \dfrac{5}{4}\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}k=\left\{0\right\}\\n=\left\{0;1\right\}\end{matrix}\right.\) \(\Rightarrow x=\left\{\dfrac{\pi}{6};-\dfrac{\pi}{2};\dfrac{3\pi}{2}\right\}\Rightarrow\dfrac{\pi}{6}-\dfrac{\pi}{2}+\dfrac{3\pi}{2}=\dfrac{7\pi}{6}\)