To solve this problem, we can use combinatorics. Let's consider the possible outcomes and favorable outcomes.
There are 9 rolls in total, and each guest gets 3 rolls. So the total number of ways to distribute the rolls is C(9,3) * C(6,3) * C(3,3), which represents choosing 3 rolls from the 9 for the first guest, then choosing 3 rolls from the remaining 6 for the second guest, and finally choosing the remaining 3 rolls for the third guest.
Now, let's consider the favorable outcomes where each guest gets one roll of each type. For the first guest, there are 3 rolls to choose from for each type, so there are 3^3 = 27 favorable outcomes. Similarly, for the second guest, there are 2 rolls of each type left, so there are 2^3 = 8 favorable outcomes. Finally, for the third guest, there is only 1 roll of each type left, so there is only 1^3 = 1 favorable outcome.
Thus, the total number of favorable outcomes is 27 * 8 * 1 = 216.
The probability that each guest gets one roll of each type is the ratio of the favorable outcomes to the total outcomes: 216 / (C(9,3) * C(6,3) * C(3,3)).
Calculating this probability and simplifying the fraction, we get:
216 / (84 * 20 * 1) = 9 / 35
Therefore, m = 9 and n = 35.
The sum m + n = 9 + 35 = 44.
Hence, the answer is 44.