In the event that the bargaining agent and the chief executive or his or her designee are unable, within thirty (30) days from and including the date of their first meeting, to reach an agreement on a contract, any and all unresolved issues shall, within three (3) days, be submitted to the state labor relations board for conciliation or fact finding. The board shall immediately appoint one of its conciliators to meet with the parties and assist in a voluntary resolution of impasses. If within ten (10) days of the conciliator’s appointment all impasses are not resolved, the conciliator shall make written findings of fact and recommendations with a view toward the voluntary settlement of unresolved issues, and the findings and recommendations shall be sent to the board and the parties. The parties shall have five (5) days in which to consider the recommendations of the conciliator and settle the unresolved issues, and any issues remaining unresolved shall be referred to binding arbitration in accordance with § 36-11-9.