\[ \boxed { {x}^{m \left ( n-1 \right ) +n}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -a \left ( y \left ( x \right ) \right ) ^{n}-b{x}^{n \left ( m+1 \right ) }=0} \]
Mathematica: cpu = 59.178515 (sec), leaf count = 90 \[ \text {Solve}\left [\int _1^{y(x) \left (\frac {a x^{-(m+1) n}}{b}\right )^{\frac {1}{n}}} \frac {1}{-K[1] \left (\frac {b^{1-n} (m+1)^n}{a}\right )^{\frac {1}{n}}+K[1]^n+1} \, dK[1]=b x^{m+1} \log (x) \left (\frac {a x^{-(m+1) n}}{b}\right )^{\frac {1}{n}}+c_1,y(x)\right ] \]
Maple: cpu = 0.187 (sec), leaf count = 61 \[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{\frac {{x}^{mn}{x}^{ n}}{-{x}^{n} \left ( {x}^{m}xb- \left ( m+1 \right ) {\it \_a} \right ) {x }^{mn}-{{\it \_a}}^{n}{x}^{m}xa}}\,{\rm d}{\it \_a}+\ln \left ( x \right ) -{\it \_C1}=0 \right \} \]