Find the following limit.\\
$\lim_{x \to -3} \frac{\frac{1}{x+6} - \frac{1}{3}}{x+3}$ \\
Give your answer as a fraction. For example, if you find that the value of the limit is $\frac{1}{2}$, you would enter $\frac{1}{2}$.\\Provide your answer below: