Subtracting Cube Roots

Let $m = \sqrt[3] {a} - \sqrt[3]{b} =\sqrt[3] {6\sqrt 3 +10} - \sqrt[3]{6\sqrt 3 -10} \\ m^3 =\,( \sqrt[3]a - \sqrt[3]b)^3 = a -b -3\sqrt[3]{ab}\,(\sqrt[3]a-\sqrt[3]b) \\ m^3 + (\sqrt[ 3]{ab})m = a-b$ Replugging the value we get $m^3 + 3(\sqrt[3]{36.3 -100}) m=20 \\ m^3 +6m -20 =0 \\ (m-2)(m^2+2m+10) =0$ Equating we have $m =2$ and $\Delta$ of quadratic equation is $<0$ so no real roots exists . Hence $m=\boxed{2}$