Nurses at 246-bed Brookside Hospital in San Pablo voted overwhelmingly to authorize a strike to back their demands for a 14% wage boost and a new two-year contract. A spokesman for the California Nurses Assn. said negotiations with hospital management have broken down and the strike will begin at the end of the month if bargaining is not resumed by then. The nurses' old contract expired July 1. Meanwhile, bargaining talks resumed in an effort to end a nurses' walkout at Providence Hospital in Oakland.