The secretary of the board of directors shall cause a notice of the filing of such petition to be published in the same manner and for the same time that notice of special elections for the issue of bonds are required by this chapter to be given. The notice shall state the filing of such petition and the names of the petitioners, a description of the lands mentioned in said petition, and the prayer of said petition, and it shall notify all persons interested in or that may be affected by such change of the boundaries of the district to appear at the office of said board at a time named in said notice, and show cause in writing, if any they have, why the change in the boundaries of said district, as proposed in said petition, should not be made. The time to be specified in the notice at which they shall be required to show cause shall be the regular meeting of the board next after the expiration of the time for the publication of the notice. The petitioners shall advance to the secretary sufficient money to pay the estimated costs of all proceedings under this chapter, however should the board of directors determine that the annexation would be of benefit to the irrigation district as a whole, the board of directors may waive payment and deposits in whole or in part for the cost of the annexation proceedings.