Having broken a connector, I found that the best tool is a fingenail: after making a very small gap between the connectors while trying to pull them apart, jam a fingernail into the imperceptably thin gap to widen it, then run that fingermail along the gap and pull the connectors while fingernails are jammed in to widen further, then they're easier to separate (rock gently while pulling, avoid pulling at the cables or flex) . Can hurt a bit.
A very small amount of silicone lubricant (avoid the pins!) helps somewhat the next time.