To simplify this expression, we first convert the mixed numbers to improper fractions:

11/15 * (9/2 : -17/5 : 17/20) + 1 11/20

Now we multiply the fraction by each number in the given fractions:

11/15 9/2 = 99/30 = 33/10
11/15 -17/5 = -187/75
11/15 * 17/20 = 187/300

Putting it all together:

33/10 + (-187/75) + 187/300 + 1 11/20

To add these fractions, we first have to get a common denominator. The least common multiple of 10, 75, and 300 is 300.

33/10 = 99/30 = 297/90
-187/75 = -748/300
187/300

Adding these fractions:

297/90 - 748/300 + 187/300 = -264/300 = -22/25

Finally, we add 1 11/20 to this result:

-22/25 + 1 11/20

Converting 1 to a fraction with denominator 20:

20/20 + 11/20 = 31/20

Therefore, the final result is:

31/20 - 22/25 = (3125 - 2220) / (20*25) = (775 - 440) / 500 = 335 / 500 = 67 / 100

So, 11/15 * (4 1/2 : -3 2/5 : 17/20) + 1 11/20 = 67/100.