If the function
\[
f(x)=\left\{
\begin{array}{ll}
\dfrac{p(1+\sin 3x)}{(\pi+6x)^2}, & -\dfrac{\pi}{2}\lt x\lt-\dfrac{\pi}{6} \\[2ex]
z, & x=-\dfrac{\pi}{6} \\[2ex]
\dfrac{q(\sin 12x+2\sin 6x)}{\cos^3\left(\frac{\pi+12x}{2}\right)}, & -\dfrac{\pi}{6}\lt x\lt 0
\end{array}
\right.
\]
is continuous at \(x=-\dfrac{\pi}{6}\), then \(p+2q=\)