To solve this problem, we first need to simplify the expressions within the parentheses before performing any additional operations.

(3/2 - 2/5)
Common denominator for 2 and 5 is 10.
(3/2)(5/5) - (2/5)(2/2)
(15/10) - (4/10)
(15 - 4) / 10
11 / 10

(3/4 + 5/6)
Common denominator for 4 and 6 is 12.
(3/4)(3/3) + (5/6)(2/2)
(9/12) + (10/12)
(9 + 10) / 12
19 / 12

Putting this together:
(11/10) + (19/12)

To add fractions, we need a common denominator which is the LCM of 10 and 12, which is 60.
(11/10)(6/6) + (19/12)(5/5)
(66/60) + (95/60)
161/60

Finally, we need to divide this sum by 19/6:
(161/60) / (19/6)
(161/60) (6/19)
(161/10) (1/19)
161/190

Therefore, the final answer is 161/190.