The factors of 6 are (6,1) and (2,3) and their reverses (1,6) and (3,2) (call the factor pair (a,b); the factors of 72 are (1,72), (2,36), (3,24), (4,18), (6,12), (8,9) and their reverses (call the factor pair (c,d). We're looking for the combination (a,b) and (c,d) such that ac-bd=+11. From this we can see that one and only one of the products ac or bd can be an odd number, which means the product of two odd numbers, and the other product must be even. The factors will be (ax+d)(bx+c), the + and - to be determined (if one is a plus, the other will be minus). An odd product reduces the possible combinations. (2,3) and (8,9) fit the requirements: 16-27=-11 giving us the factors (2x-9)(3x+8).
So the dimensions of the rectangle are 2x-9 and 3x-8.