Suppose that $f$ is a polynomial and $h$ is a polynomial of degree $5$ or less such that\[(x^2+3x-3)\cdot f(x)+h(x)= -6x^6+72x^4 -50x^3 + 13

Suppose that $f$ is a polynomial and $h$ is a polynomial of degree $5$ or less such that\[(x^2+3x-3)\cdot f(x)+h(x)= -6x^6+72x^4 -50x^3 + 13x^2 +38x -44.\]What is the degree of $f$?