A petition for any private act shall not be received or acted upon by the General Assembly unless 1 month's notice of the intention to present such petition has either been served in writing upon the person or persons to be affected by such act or published in a newspaper published within the county of the petitioner's residence, if there is one or, if there is none, then in a newspaper published within the State. Proof of such notice may be dispensed with if the object of the petition is of such nature that no person other than the petitioner can be affected thereby.