Answer
$10$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $ (\sqrt[3]{11}-1)(\sqrt[3]{11^2}+\sqrt[3]{11}+1) ,$ use the factoring of the difference of $2$ cubes.
$\bf{\text{Solution Details:}}$
Using the factoring of the difference of $2$ cubes which is given by $a^3-b^3=(a-b)(a^2+ab+b^2),$ the expression above is equivalent\begin{array}{l}\require{cancel} (\sqrt[3]{11})^3-(1)^3 \\\\= 11-1 \\\\=
10
.\end{array}
