Step 1 :Given three polynomials: \(7x^{3} - 14x^{2} + 6x + 11\), \(-5x^{3} + 9x^{2} - x + 25\), and \(-x^{3} - x^{2} - 4x - 1\).
Step 2 :To add these polynomials together, we need to add the coefficients of the like terms together. The like terms are the terms that have the same variable and exponent.
Step 3 :Adding the coefficients of the \(x^{3}\) terms: \(7 - 5 - 1 = 1\).
Step 4 :Adding the coefficients of the \(x^{2}\) terms: \(-14 + 9 - 1 = -6\).
Step 5 :Adding the coefficients of the \(x\) terms: \(6 - 1 - 4 = 1\).
Step 6 :Adding the constant terms: \(11 + 25 - 1 = 35\).
Step 7 :So, the sum of the polynomials is \(x^{3} - 6x^{2} + x + 35\).
Step 8 :Final Answer: The sum of the polynomials is \(\boxed{x^{3} - 6x^{2} + x + 35}\).