I'm looking for a job in a foreign country in the EU. Should I mention right away in my resume or cover letter that I have no work permit in their country and therefore need a visa sponsorship? My resume states my home address which is outside the target country, but it does not say anything about permits. I hope to get a remote interview but I'm afraid that mentioning the lack of permit may deter the employers and they won't even give me a chance.
I only apply to job postings on the internet that don't explicitly disallow foreigners, but they usually don't promise any sponsorship either.