Upon the filing of a petition with the Board of County Commissioners for a change of boundary lines of any sewer improvement district signed by a majority of the holders of title to lands of the area proposed to be annexed to an adjacent sewer improvement district, the Board of County Commissioners shall cause notice to be published one (1) time in some newspaper printed and published in the county and of general circulation in the area sought to be annexed at least ten (10) days before the time at which such petition will be considered. Such notice shall state the time and place when and where the petition will be considered by the Board of County Commissioners, a brief substance of the petition, and that all persons interested may appear and be heard. The Board of County Commissioners shall have exclusive jurisdiction to hear and determine all contests and objections pertaining to such annexation, and at the time set for hearing the Board may amend the plan of annexation by excluding from within its boundaries lands which it may deem will not be benefited by annexation to such sewer improvement district. At such hearing the Board shall also determine whether or not the annexation of such area to such sewer improvement district will be to the best interests of the holders of title of the area affected, or conducive or beneficial to the public health of said area as now exists or to be developed and if said Board determines that it will, then it shall make an order annexing such area to said improvement district, and such territory for all purposes shall thereafter be a part of such sewer improvement district. The annexed territory shall assume its full proportion of all legal indebtedness outstanding against the original sewer improvement district, including bonded indebtedness.