From the two-way table, the total number of students who said "No" is $267$. The row totals give us:

$65 + x + y + 56 = 267$

$x + y = 146$

Using the additional constraint from the table (the column total for 11th graders or another given total), we can solve for $x$.

The conditional probability $P(\text{11th grade} \mid \text{No}) = \frac{y}{267}$ and the given information yields:

$x = 71$