To solve this problem, we first need to simplify the expression inside the parentheses:

(1/6 + 1/10 + 1/15) = (5/30 + 3/30 + 2/30) = 10/30 = 1/3

(3/5 - 1/3 - 1/4) = (12/20 - 20/60 - 15/60) = (36/60 - 20/60 - 15/60) = 1/60

Now we can divide 1/3 by 1/60:

(1/3) / (1/60) = (1/3) * (60/1) = 60/3 = 20

Therefore, the value of the expression is 20.