To add these fractions, we need to find a common denominator. The least common denominator (LCD) of 15, 35, 36, 99, and 143 is 2520.

Now, we can rewrite each fraction with the LCD as the denominator:

1/15 = (1/15) * (168/168) = 168/2520
1/35 = (1/35) * (72/72) = 72/2520
1/36 = (1/36) * (70/70) = 70/2520
1/99 = (1/99) * (40/40) = 40/2520
1/143 = (1/143) * (18/18) = 18/2520

Now, we can add the fractions:

168/2520 + 72/2520 + 70/2520 + 40/2520 + 18/2520

To add fractions with the same denominator, we simply add the numerators:

(168 + 72 + 70 + 40 + 18)/2520

= 368/2520

Now, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 8:

(368/8)/(2520/8)

= 46/315

Therefore, the sum of the fractions is 46/315.