Let \( k\in \mathbb{R} \). If \( \displaystyle \lim_{x\to 0^{+}}\left(\sin(\sin kx)+\cos x+x\right)^{\frac{2}{x}}=e^{6} \), then the value of \( k \) is:
\( 1 \)
\( 2 \)
\( 3 \)
\( 4 \)
