Expected Value, Linearity & Advanced Probability · Superchallenge problem

In an election, candidate $A$ receives $7$ votes and $B$ receives $4$ votes. The $11$ ballots are counted one at a time in uniformly random order. Find the probability that $A$ is strictly ahead of $B$ throughout the count.

The answer is a fraction $\tfrac{m}{n}$ in lowest terms; find $m + n$.