将函数$y=\sin x$的图象上各点横坐标缩短为原来的$\dfrac{1}{2}$,再向左平移$\dfrac{\pi}{6}$个单位长度得到函数$y=f(x)$的图象,当$x\in\left[-\dfrac{\pi}{3},\dfrac{\pi}{6}\right]$时,$f(x)$的值域为（ ）.
A. $[-1,1]$
B. $\left[-\dfrac{\sqrt{3}}{2},\dfrac{\sqrt{3}}{2}\right]$
C. $\left[-\dfrac{\sqrt{3}}{2},1\right]$
D. $\left[-\dfrac{1}{2},1\right]$