You'll have to email local bitcoins support and tell them you sent bitcoin cash to that address...
If they tell you its impossible for them to recover it, then they're jut outright lying... They may not want to recover it but you might be able to keep emailing them to a point where they do (they'll have engineers at least to be able to do it).
If the amount is low enough, they will probably not want to help because it wouldn't be worth the effort.
I'm not sure if this applies to OP's problem, but:
Custom work, e.g. research of possible external problems, is 200 EUR/hour paid in Bitcoin at the current market rate. Minimum billable amount is 200 EUR.
(source:
https://localbitcoins.com/fees)
From what I understand, they ask you 200 EUR if you need help with
external problems. I think sending to the wrong chain is considered external.
Best thing you can do is email them like @jackg said, and ask them if they could either give you the necessary private keys or if they could help in any way. Give it a try..