To solve this problem, we can start by setting up an equation based on the given information.

Let's assume the fraction is represented by 'x'.

According to the problem, 6 times the fraction is greater than 7 times its reciprocal by 11. We can express this as:

6x > 7(1/x) + 11

Now, let's simplify the equation step by step to solve for 'x'.

Simplifying the right side of the equation:
7(1/x) + 11 = 7/x + 11

Finding a common denominator:
7/x + 11 = (7 + 11x) / x

Substituting the simplified expression back into the equation:
6x > (7 + 11x) / x

Multiplying both sides of the equation by 'x' to eliminate the denominator:
6x^2 > 7 + 11x

Rearranging the equation to isolate the terms on one side:
6x^2 - 11x - 7 > 0

Now we have a quadratic inequality. To solve it, we can factor the expression or use the quadratic formula.

Factoring the quadratic expression:
(2x - 7)(3x + 1) > 0

Setting each factor greater than zero to find the intervals where the inequality is satisfied:
2x - 7 > 0 or 3x + 1 > 0

Solving each inequality separately:
2x > 7 or 3x > -1

x > 7/2 or x > -1/3

Since we are looking for a fraction, the value of 'x' cannot be negative. Therefore, we discard the interval x > -1/3.

So, the solution is x > 7/2, which means the fraction is greater than 7/2.

Among the given answer choices, the only fraction that satisfies this condition is 7/3 (option B).

Therefore, the correct answer is option B, 7/3.