已知 $y=f\left(x\right)=\frac{1}{\sqrt[3]{{(x+1)}^2}+\sqrt[3]{x^2+x}+\sqrt[3]{x^2}}$，则 $f\left(1\right)+f\left(2\right)+\cdots +f\left(511\right)=$＿＿＿＿＿．