Whenever, in the judgment of the district board, a system of drainage, sanitary sewers, or sewage disposal or treatment plants for any lands included in the operation of the district will be of special benefit to the lands of the district as a whole, it shall pass a resolution to that effect and call a further meeting of the board to determine the question. Notice of said meeting shall be given by the secretary for the same length of time and in the same manner as required by law for the meeting of the county board to hear the petition for the organization of the district. At the time and place mentioned in the notice the board shall meet, hear such evidence as shall be presented, and fully determine the matter by resolution which said resolution shall be final and conclusive upon all persons as to the benefit of said system of drainage, sanitary sewers, or sewage disposal or treatment plants to the lands in the district.