The first equation can be factorized into $$x^4y^4(x+y)=810\implies x+y=\frac{810}{x^4y^4}$$ Applying this to the second equation gives $$x^3y^3(x+y)((x+y)^2-3xy)=945\implies \Big(\frac{x}{y}-1+\frac{y}{x}\Big)=\frac{7}{6}\implies \frac{x}{y}=\frac{3}{2},\frac{2}{3}$$ By symmetry, we can assume $x:y=3:2$. Plugging this into the first given equation leads to $$(x,y)=\Big(2^{\frac{2}{3}},\frac{3\cdot 2^{\frac{3}{2}}}{2}\Big)$$ Setting these to the target question gives the answer as $\boxed{89}$.