Most caridina shrimp won't breed with red cherries, which are neocaridinas.
Here is a good resource about shrimp and interbreeding. According to the chart it has, the only shrimp that will interbreed with red cherries (there may be some species left out on the chart, and some of the common names are not specific) are blue pearls (neos), neo. heterop, red tigers (neos) and yellow neos.
Here is the complete interbreeding chart, in case you want to see more species.
An important thing to consider when putting multiple shrimp in the same tank is water parameters. Many of the neocaridina species tolerate a wide range of ph, gh and kh. Many of the caridina species (crystal reds for example) are less tolerant and usually need softer water. Many people have been successful in acclimating crystal reds (and other caridinas) into harder water and breeding them, but it doesn't work for everyone.