Laundry washing machine (1) comprising an outer casing (2) and, inside said casing (2), a washing tub (3) arranged inside said casing (2) directly facing a laundry loading/unloading opening realized in a front wall (2a) of said casing (2); a rotatable drum arranged in axially rotating manner inside the washing tub (3) and structured for receiving the laundry to be washed; an detergent dispenser (9) which is structured for supplying detergent into the washing tub (3); and a water softening device (11) which is structured for reducing the hardness degree of the fresh water supplied to the washing tub (3); the water softening device (11) in turn comprising a water-softening agent container (23) filled with a water softening agent able to reduce the hardness degree of the fresh water supplied to the washing tub (3), and a regeneration-agent reservoir (21) which is fluidly connected to said water-softening agent container (23) and is structured to receive a salt or other regeneration agent for performing a regener
