To solve this expression, we can follow the order of operations (PEMDAS).

Step 1: Simplify the expression inside the parentheses first.
8 3/4 = 35/4
6 1/2 = 13/2
Adding 35/4 - 13/2 = 35/4 - 26/4 = 9/4

Next, convert the denominators to a common denominator. The common denominator would be 4.
9/4 - 6/4 = 3/4

Step 2: Divide this result by 1/8 and then add 11 3/7.
(3/4 ÷ 1/8) + 11 3/7
(3/4 * 8) + 11 3/7
(24/4) + 11 3/7
6 + 11 3/7
6 + 80/7
6 + 11 3/7 = 17 3/7

Step 3: Subtract this result from 30.
30 - 17 3/7
30 - (7*17 + 3) /7
30 - (119 + 3) / 7
30 - 122 / 7
30 - 17 3/7 = 12 4/7 or 12.5714

Therefore, the final result is approximately 12.5714