已知双曲线\(C：\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}=1(a>0,b>0)\)的左，右焦点分别为\(F_{1}\)，\(F_{2}\)，以原点\(O\)为圆心，\(OF_{1}\)为半径的圆与双曲线\(C\)在第一象限交于点\(A\)，若\(∠OAF_{1}=\dfrac{π}{6}\)，则双曲线\(C\)的离心率为\((\quad)\)
A. \(\sqrt{2}\)
B. \(\sqrt{2}+1\) C. \(\sqrt{3}\) D. \(\sqrt{3}+1\)
