If the local maximum value of the function \( f(x)=\left(\dfrac{\sqrt{3}e}{2\sin x}\right)^{\sin^2 x},\ x\in\left(0,\dfrac{\pi}{2}\right), \) is \( \dfrac{k}{e} \), then \( \left(\dfrac{k}{e}\right)^8+\dfrac{k^8}{e^5}+k^8 \) is equal to:
\( e^3+e^6+e^{11} \)
\( e^3+e^6+e^{10} \)
\( e^5+e^6+e^{11} \)
\( e^3+e^5+e^{11} \)
