To add these fractions together, we need to find a common denominator first. In this case, the common denominator is 30.

5/6 = 25/30
15/6 = 45/30
19/6 = 95/30

2 4/10 = 2 12/30
1 7/10 = 1 21/30
21/10 = 63/30

Now, adding all the fractions together:

25/30 + 45/30 + 95/30 + 2 12/30 + 1 21/30 + 63/30
= (25 + 45 + 95 + 230 + 130 + 63)/30
= (25 + 45 + 95 + 60 + 30 + 63)/30
= 318/30

Now, we can simplify the sum by dividing both the numerator and denominator by their greatest common divisor, which is 6:

318 ÷ 6 = 53
30 ÷ 6 = 5

Therefore, the simplified sum of the fractions is 53/5 or 10 3/5.