已知函数$f(x)=\sin(\omega x+\varphi)$在区间$\left(\dfrac{\pi}{6},\dfrac{2\pi}{3}\right)$单调递增,直线$x=\dfrac{\pi}{6}$和$x=\dfrac{2\pi}{3}$为函数$y=f(x)$的图象的两条对称轴,则$f\left(-\dfrac{5\pi}{12}\right)=$（ ）
A
$-\dfrac{\sqrt{3}}{2}$
B
$-\dfrac{1}{2}$
C
$\dfrac{1}{2}$
D
$\dfrac{\sqrt{3}}{2}$
E
F