We can group like terms and combine them to simplify the expression:
$(x^3+4x^2-7x+11)+(-4x^4-x^3+x^2+7x+3) = -4x^4 + (x^3 - x^3) + (4x^2 + x^2) + (-7x + 7x) + (11 + 3) = \boxed{-4x^4 + 5x^2 + 14}.$
The answer is: -4x^4+5x^2+14
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Simplify $$(x^3+4x^2-7x+11)+(-4x^4-x^3+x^2+7x+3).$$  Express your answer as a polynomial with the terms in order by decreasing degree.

### Answer:
