[Ne[S]zA]

$$\lim_{x \to -2} \dfrac{2x^2+x-6}{\sqrt[3]{6-x}-2\sqrt[3]{3x+7} }=\lim_{x \to -2} \dfrac{2x^2+x-6}{\sqrt[3]{6-x}-\sqrt[3]{24x+56} }$$
$$=\lim_{x \to -2} \dfrac{2x^2+x-6}{\sqrt[3]{6-x}-2\sqrt[3]{3x+7} } \cdot \dfrac{(6-x)^{2/3}+(6-x)^{1/3}(24x+56)^{1/3}+(24x+56)^{2/3}}{(6-x)^{2/3}+(6-x)^{1/3}(24x+56)^{1/3}+(24x+56)^{2/3}}$$
$$=\lim_{x \to -2} \dfrac{(2x-3)(x+2)}{-25(x+2)} \cdot[ (6-x)^{2/3}+(6-x)^{1/3}(24x+56)^{1/3}+(24x+56)^{2/3}]=\dfrac{-7}{-25}\cdot (4+2\cdot 2+4)=\dfrac{84}{25}$$