We introduce a new integrable equation valued on a Cayley-Dickson (C-D) algebra. In the particular case in which the algebra reduces to a complex one the new interacting term in the equation cancels and the equation becomes the known Korteweg-de Vries (KdV) equation. For each C-D algebra the equation has an infinite sequence of local conserved quantities. We obtain a Backlund transformation in the sense of Walhquist-Estabrook for the equation for any Cayley-Dickson algebra, and relate it to a generalized Gardner equation. From this, the infinite sequence of conserved quantities follows directly, we give the explicit expression for the first few. From the Backlund transformation we get the Lax pair and the one-soliton and two-soliton solutions generalizing the known solutions for the quaternion valued KdV equation. From the Gardner equation we obtain the generalized modified KdV equation which also has an infinite sequence of conserved quantities. The new integrable equation is preserved under a subgroup of the automorphisms of the C-D algebra. In the particular case of the algebra of octonions, the equation is invariant under SU(3).