函数$f(x)=\cos(\omega x+\varphi)(\omega>0,0 < \varphi < x)$的最小正周期$T=\dfrac{2\pi}{3}$,其图象关于$\left(\dfrac{\pi}{18},0\right)$对称,且当$x\in\left[\dfrac{\pi}{6},m\right]$时,$f(x)$的值域为$\left[-1,-\dfrac{\sqrt{3}}{2}\right]$,则$m$的取值范围为（ ）.
A. $\left[\dfrac{\pi}{9},\dfrac{7\pi}{18}\right]$
B. $\left[\dfrac{2\pi}{9},\dfrac{7\pi}{18}\right]$
C. $\left[\dfrac{\pi}{9},\dfrac{5\pi}{18}\right]$
D. $\left[\dfrac{2\pi}{9},\dfrac{5\pi}{18}\right]$