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It depends on the user's settings.

If it was possible, it's not anymore. I just went through, there's only the option of allowing "InMail"

https://www.linkedin.com/help/linkedin/answer/1584 says InMail allows you to directly message another LinkedIn member that you're not connected to.

Note: If you have a Basic (free) account, you can only directly message LinkedIn members that you’re connected to. You must upgrade to a Premium account to use InMail

I just send a friend request accompanied with a short introduction. It worked last October, but I haven't tried since.

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