Rút gọn biểu thức
a) \(\sqrt[3]{{{x^3} + 1 + 3x\left( {x + 1} \right)}}\);   b) \(\frac{{x + 1}}{{\sqrt[3]{{{x^2}}} - \sqrt[3]{x} + 1}}\).

a). \[\sqrt[3]{{27}} - \sqrt[3]{{ - 8}} - \sqrt[3]{{125}} = \sqrt[3]{{{3^3}}} - \sqrt[3]{{{2^3}}} - \sqrt[3]{{{5^3}}} = 3 + 2 - 5 = 0\]

b). \[\frac{{\sqrt[3]{{135}}}}{{\sqrt[3]{5}}} - \sqrt[3]{{54}}.\sqrt[3]{4}. = \sqrt[3]{{\frac{{135}}{5}}} - \sqrt[3]{{54.4}}. = \sqrt[3]{{27}} - \sqrt[3]{{216}} = 3 - 6 =  - 3\]

Ta có: \[\sqrt[3]{{512}} = \sqrt[3]{{{8^3}}} = 8.\]

\[\sqrt[3]{{ - 729}} = \sqrt[3]{{ - {9^3}}} =  - 9.\]

\[\sqrt[3]{{0,064}} = \sqrt[3]{{{{(0,4)}^3}}} = 0,4.\]

\[\sqrt[3]{{ - 0,216}} = \sqrt[3]{{{{( - 0,6)}^3}}} =  - 0,6.\]

\[\sqrt[3]{{ - 0,008}} = \sqrt[3]{{{{( - 0,2)}^3}}} =  - 0,2.\]