Since the degree of the numberator and the denominator are the same you need to use long division before partial fractions!

Remember that if the degree of the numerator is greater than or equal to the denominator ALWAYS use long division.

I don't know how to write out long division with LaTex but

$\displaystyle \frac{-x^2-x-1}{5x^2+7x-6}=-\frac{1}{5}+\frac{\frac{2}{5}x-\frac{11}{5}}{5x^2+7x-6}=-\frac{1}{5}+\frac{1}{5}\left( \frac{2x- 11}{5x^2+7x-6} \right)$

Now we can use partial fractions on $\displaystyle \left( \frac{2x- 11}{5x^2+7x-6} \right)$

Good luck