All state lands granted, sold or leased since the fifteenth day of June, 1911, or hereafter granted, sold or leased, containing timber, minerals, stone, sand, gravel, or other valuable materials, or when other state lands contiguous or in proximity thereto contain any such valuable materials, shall be subject to the right of the state, or any grantee or lessee thereof who has acquired such other lands, or any such valuable materials thereon, since the fifteenth day of June, 1911, or hereafter acquiring such other lands or valuable materials thereon, to acquire the right-of-way over such lands so granted, sold or leased, for private railroads, skid roads, flumes, canals, watercourses or other easements for the purpose of, and to be used in, transporting and moving such valuable materials from such other lands, over and across the lands so granted or leased, upon the state, or its grantee or lessee, paying to the owner of lands so granted or sold, or the lessee of the lands so leased, reasonable compensation therefor. In case the parties interested cannot agree upon the damages incurred, the same shall be ascertained and assessed in the same manner as damages are ascertained and assessed against a railroad company seeking to condemn private property.