\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {{b}^{3}+ \left ( y \left ( x \right ) \right ) ^{2}{b}^{3}+2\,y \left ( x \right ) {b}^{2}ax+{x}^{2}b{a}^{2}+ \left ( y \left ( x \right ) \right ) ^{3}{b}^{3}+3\, \left ( y \left ( x \right ) \right ) ^{2}{b}^{2}ax+3\,y \left ( x \right ) b{a}^{2}{x}^{2}+{a}^{3}{x}^{3}}{{b}^{3}}}=0} \]
Mathematica: cpu = 0.155520 (sec), leaf count = 145 \[ \text {Solve}\left [-\frac {1}{3} (27 a+29 b)^{2/3} \text {RootSum}\left [\text {$\#$1}^3 (27 a+29 b)^{2/3}-3 \text {$\#$1} b^{2/3}+(27 a+29 b)^{2/3}\& ,\frac {\log \left (\frac {\frac {3 a x+b}{b}+3 y(x)}{\sqrt [3]{\frac {27 a+29 b}{b}}}-\text {$\#$1}\right )}{b^{2/3}-\text {$\#$1}^2 (27 a+29 b)^{2/3}}\& \right ]=\frac {1}{9} x \left (\frac {27 a+29 b}{b}\right )^{2/3}+c_1,y(x)\right ] \]
Maple: cpu = 0.047 (sec), leaf count = 42 \[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( {{\it \_a}}^{3}b+{{\it \_a}}^{2}b+a+b \right ) ^{-1}{d{ \it \_a}}b-x+{\it \_C1} \right ) b-ax}{b}} \right \} \]