Yes, Cymbalta is an snri and Prozac an ssri. As they both target serotonin, it would be very unusual to combine them, as the above post makes clear. Because docs and psychiatrists often do very strange things with drugs, if you've been prescribed both of these it would be good to find out why and make sure the doc knows what he or she is doing.
Talk to your doctor before using FLUoxetine together with DULoxetine. Combining these medications can increase the risk of a rare but serious condition called the serotonin syndrome, which may include symptoms such as confusion, hallucination, seizure, extreme changes in blood pressure, increased heart rate, fever, excessive sweating, shivering or shaking, blurred vision, muscle spasm or stiffness, tremor, incoordination, stomach cramp, nausea, vomiting, and diarrhea. Severe cases may result in coma and even death. You should contact your doctor immediately if you experience these symptoms while taking the medications. It is important to tell your doctor about all other medications you use, including vitamins and herbs. Do not stop using any medications without first talking to your doctor
Found this online.
I would call a local pharmacy and ask. I dont know for sure but do not think they can be taken together.