\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {{a}^{3}+ \left ( y \left ( x \right ) \right ) ^{2}{a}^{3}+2\,y \left ( x \right ) {a}^{2}bx+a{b}^{2}{x}^{2}+ \left ( y \left ( x \right ) \right ) ^{3}{a}^{3}+3\, \left ( y \left ( x \right ) \right ) ^{2}{a}^{2}bx+3\,y \left ( x \right ) a{b}^{2}{x}^{2}+{b}^{3}{x}^{3}}{{a}^{3}}}=0} \]
Mathematica: cpu = 0.160520 (sec), leaf count = 145 \[ \text {Solve}\left [-\frac {1}{3} (29 a+27 b)^{2/3} \text {RootSum}\left [\text {$\#$1}^3 (29 a+27 b)^{2/3}-3 \text {$\#$1} a^{2/3}+(29 a+27 b)^{2/3}\& ,\frac {\log \left (\frac {\frac {a+3 b x}{a}+3 y(x)}{\sqrt [3]{\frac {29 a+27 b}{a}}}-\text {$\#$1}\right )}{a^{2/3}-\text {$\#$1}^2 (29 a+27 b)^{2/3}}\& \right ]=\frac {1}{9} x \left (\frac {29 a+27 b}{a}\right )^{2/3}+c_1,y(x)\right ] \]
Maple: cpu = 0.047 (sec), leaf count = 42 \[ \left \{ y \left ( x \right ) ={\frac {{\it RootOf} \left ( \int ^{{\it \_Z}}\! \left ( {{\it \_a}}^{3}a+{{\it \_a}}^{2}a+a+b \right ) ^{-1}{d{ \it \_a}}a-x+{\it \_C1} \right ) a-bx}{a}} \right \} \]