Air carrier flight crew reported fuel imbalance in cruise. Flight crew landed uneventfully at destination.

Narrative

FLIGHT XXX from ZZZ to ZZZ1 in Aircraft X we experienced a severe fuel imbalance. MEL-XX-XX-XX center tank systems PUMPS had been applied to the aircraft and all operational procedures were complied with. Once the center was empty the fuel cross feed was selected Off. There is a note in the MEL which says NOTE: In certain situations; it is possible for a fuel imbalance to develop while operating under the Procedure guidance for this MEL. Monitor fuel load to ensure a significant imbalance does not occur." After the center tank emptied we completed the MEL Procedure to turn off the cross feed and a systems check showed both left and right tanks were within 100 lbs of each other. Our attention was then diverted due to weather that required multiple deviations to avoid. Shortly after we cleared the weather we were alerted to the imbalance situation by a Fuel L Wing TK LO LVL ECAM. Followed by a. FUEL IMBALANCE ECAM. The fuel page displayed 1420lbs in the left tank and 12100 in the right tank. We ran the fuel imbalance QRH and landed with 1420 lbs in the left tank and approximately 6000 lbs in the right tank. There were no controllability issues throughout the landing sequence. We were so focused on the WX radar and the weather outside the aircraft for that the last hourly systems check for was approximately an hour and a half before we got the ECAMS."