Any person claiming to be injured within the boundaries of a designated groundwater basin by any act of the state engineer or commission under the provisions of this article, or the failure of the state engineer or commission to take any action under the provisions of this article, except as provided for the small capacity wells in section 37-90-105, shall file a written petition with the commission stating the basis of the alleged injury. Thereafter, only upon request by a petitioner and upon thirty-five days' written notice to any adverse party, the commission shall conduct a hearing upon the petition in the manner provided in section 37-90-113. If notice of any such act has been published pursuant to section 37-90-112 and no hearing has been requested pursuant to such notice, this section shall not be construed to create a subsequent or additional right to request a hearing concerning such act.