To solve this expression, we first simplify the innermost parentheses:

7/18 + 2/27 = 7/18 + 2/27 = 21/54 + 4/54 = 25/54

Next, we add 1/6 to the result:

1/6 + 25/54 = 9/54 + 25/54 = 34/54

Now we divide by 5/9:

34/54 ÷ 5/9 = 34/54 * 9/5 = 306/270 = 17/15

Next, we simplify the expression 3/11 * 2:

3/11 * 2 = 6/11

Now, we add this result to 17/15:

17/15 + 6/11 = 187/165 + 90/165 = 277/165

Finally, we add 277/165 to 1 1/5:

1 1/5 = 6/5

Now, we add:

277/165 + 6/5 = 277/165 + 198/165 = 475/165

So, the final answer is 475/165.