Megan is jealous of her older sister's $a\times b$ inch Zac Efron poster, so she cuts out a rectangle around his face, which has dimensions $\frac{a}{2}-2$ by $\frac{b}{3}-5$, and steals it. Megan's older sister decides she's over Zac Efron anyways, and uses the rest of the paper as wrapping paper. She wraps an $11$-inch cube, wasting no paper, and has $3$ square inches leftover. If $a$ and $b$ are integers and $b>a$, and the difference between the length and width of the poster is less than $50$, find the dimensions of the poster. Express your answer as the ordered pair $(a, b)$.