Let $f(x)=\frac{\sqrt[\phantom{2}]{9x^6-x}}{x^3+1}$

$($a$)$ Make a table of values of $f$ to estimate $\underset{x-}{lim}\frac{\sqrt[\phantom{2}]{9x^6-x}}{x^3+1}.$

$($b$)$ Find $\underset{x-}{lim}\frac{\sqrt[\phantom{2}]{9x^6-x}}{x^3+1}$ algebraically.