Calculus for Combinatorics

$\sum_{r=0}^{10} \left( (-1)^r \left( \frac{1}{r+1}+ \frac{1}{r+2}+ \cdots +\frac{1}{r+10} \right) \binom{10}{r} \right)$

The sum above can be expressed as $\dfrac{a}{b}$ , where $a$ and $b$ are coprime positive integers.

Find $(a+b)$ .