$Thedomainofthefunctionf\left(x\right)=\sqrt[3]{\frac{2x-1}{x^2-10x-11}}is$

$\begin{array}{l}f\left(x\right)=\sqrt[3]{\frac{2x-1}{x^2-10x-11}}isdefinediff\\ x^2-10x-11\ne 0\\ \Rightarrow x^2-11x+x-11\ne 0\\ \Rightarrow x\left(x-11\right)+1\left(x-11\right)\ne 0\\ \Rightarrow \left(x+1\right)\left(x-11\right)\ne 0\\ \Rightarrow x\ne -1,11\\ \therefore x\in \left(-\infty ,-1\right)\cup \left(-1,11\right)\cup \left(11,\infty \right)\end{array}$