To add these two mixed numbers, we need to first convert them to improper fractions and then add them together.

(12-1 5/9) = (11 4/9) = (11*9 + 4) / 9 = 103 / 9

(7-2 11/18) = (4 7/18) = (4*18 + 7) / 18 = 79 / 18

Now, we add the two improper fractions together:

103/9 + 79/18

To add these fractions, we need to find a common denominator. The least common multiple of 9 and 18 is 18.

So, we rewrite the fractions with a common denominator:

(103/9) * (2/2) = 206/18
(79/18)

Now add the two fractions together:

206/18 + 79/18 = 285/18

Finally, we convert the sum back to a mixed number:

285 / 18 = 15 15/18

Therefore, (12-1 5/9) + (7-2 11/18) = 15 15/18, which simplifies to 15 5/6.