It wasn’t easy for Chantel Mendez and Tamir Capehart to rearrange their work schedules and trek more than an hour on a recent Tuesday morning to join a protest at the governor’s mansion on behalf of the workers in their fast-growing industry. Mendez, from Bridgeport, and Capehart, from Norwich, are among 11,000 personal care attendants for elderly or disabled clients on Medicaid. As independent contractors, they technically work directly for their clients, part of the vast army of people toiling in home-care for various client groups.