One2lead is a chrome plugin with which one can automatically send a message to a list of contacts in LinkedIn. It also has features to do a follow up (drip campaign). One2Lead also gathers contact information.
step 1) do a search in Linkedin.
step 2) at the contact to Mautic
step3) setup a campaign and send a message from mautic over LinkedIn (inmail or invite)
Alternatively:
Step 1) import in Mautic contacts with URL to their LinkedIn page (create an extra field in Mautic)
Step2) setup a campaign and send the inmails or invites