To add these two fractions, we first need to find a common denominator.

6 1/14 = (6 * 14 + 1) / 14 = 85 / 14

1 5/7 = (1 * 7 + 5) / 7 = 12 / 7

Now, we add the fractions:

85/14 + 12/7

To find a common denominator, we multiply the denominators together:

14 * 7 = 98

Now, we rewrite the fractions with the common denominator:

85/14 * 7/7 = 595/98

12/7 * 14/14 = 168/98

Now we add the fractions:

595/98 + 168/98 = 763/98

Therefore, (6 1/14) + (1 - 5/7) = 763/98 or 7 39/98.