Whenever the board of directors of any levee district shall ascertain that the levees constructed by said district are insufficient, from any cause, to afford complete protection from overflows, to the lands in said district, they may by resolution entered upon the record of said levee board call a meeting of the landowners of said levee district to be held at some convenient place on the line of said levee, for the purpose of determining whether said levee shall be enlarged and strengthened; and they shall give the same notice as required in the case of calling a landowners’ meeting in the organization of a new district, as provided by section 245.460, and at such meeting they shall lay before the landowners present an estimate of the cost of the proposed work of enlarging and strengthening said levee, made by an engineer, and a vote shall be taken at such meeting, by the landowners present, voting either by themselves or by proxy, whether an additional tax shall be levied and an additional percent of the assessed benefits expended for such purpose, and if a majority of the votes cast are in favor of such additional work the board shall proceed to construct the same and the additional taxes may be levied and apportionment of benefits made as herein provided.