Manuel says that you can use one of the denominators of 5 / 6 and 11/30 when renaming these fractions using a common denominator. why is this true?

It is true because 5/6 and 11/30 have a common denominator of 30. a common denominator is the bottom number of the fraction that will make it easy to add the two fractions.
example: 2/7 and 3/14 have a common denominator of 14 because you can multiple 2/7 by 2 to get an equivalent fraction of 4/14. now the denominator is the same and you can add the two fractions