If you take the two addends and combine the tens digit of one with the units digit of the other, and vice versa, they will of course add up to the same 2-digit number as before. But in addition, for these chosen numbers, the two mixed numbers (the new addends) are each also the product of two primes, and these six primes also are all different, but may contain repeats from the first set of six.

What are the numbers involved?