Parrot chooses a three-digit positive integer
and writes both its base-5 and base-6 representations on a blackboard. Later Wemmbu sees the two numbers Parrot has written. Treating the two numbers as base-10 integers, he adds them to obtain an integer
. For example, if
, Parrot writes the numbers
and
, and Wemmbu obtains the sum
. For how many choices of
are the two rightmost digits of
, in order, the same as those of
?