In the $x y$-plane, points $P(1,1), Q(2,6)$, and $R(6,8)$ are three vertices of a parallelogram $P Q R S$. What is the sum of the slopes of the sides of the parallelogram?

Step 1 ：In the $x y$-plane, points $P(1,1), Q(2,6)$, and $R(6,8)$ are three vertices of a parallelogram $P Q R S$.

Step 2 ：The sum of the slopes of the sides of a parallelogram is zero. This is because opposite sides of a parallelogram are parallel, and parallel lines have the same slope.

Step 3 ：Therefore, the sum of the slopes of the sides of the parallelogram is the sum of the slopes of two pairs of parallel lines, which is zero.

Step 4 ：Final Answer: The sum of the slopes of the sides of the parallelogram is \(\boxed{0}\).