To add these fractions, we need to find a common denominator. The least common multiple of 6 and 14 is 42.

Therefore, we need to rewrite the fractions with a common denominator of 42:

5/6 = 35/42
3/14 = 9/42

Now we can add the fractions together:

35/42 + 9/42 = 44/42

Finally, we can simplify the fraction:

44/42 = 22/21

Therefore, 5/6 + 3/14 = 22/21