如图，在平面直角坐标系\(xOy\)中，点\(A(x_{1},y_{1})\)在单位圆\(O\)上，\(∠xOA=α\)，且\(α∈( \dfrac {π}{6}, \dfrac {π}{2}).\)
\((1)\)若\(\cos (α+ \dfrac {π}{3})=- \dfrac {11}{13}\)，求\(x_{1}\)的值；
\((2)\)若\(B(x_{2},y_{2})\)也是单位圆\(O\)上的点，且\(∠AOB= \dfrac {π}{3}.\)过点\(A\)、\(B\)分别做\(x\)轴的垂线，垂足为\(C\)、\(D\)，记\(\triangle AOC\)的面积为\(S_{1}\)，\(\triangle BOD\)的面积为\(S_{2}.\)设\(f(α)=S_{1}+S_{2}\)，求函数\(f(α)\)的最大值．