To solve the given expression:

$\sqrt[3]{110 - 137} + 4(-5)^2$

Step-by-step Solution:

1. Simplify inside the cube root:
   $110 - 137 = -27$

   So, the expression becomes:
   $\sqrt[3]{-27} + 4(-5)^2$

2. Cube root of $-27$:
   The cube root of $-27$ is $-3$:
   $\sqrt[3]{-27} = -3$

3. Square $-5$:
   $(-5)^2 = 25$

4. Multiply by 4:
   $4 \cdot 25 = 100$

5. Add the results:
   $-3 + 100 = 97$

Final Answer:

The value of the expression is 97.

Let me know if you want further details or clarification!

Here are some related questions you might find helpful:

1. What is a cube root, and how do you calculate it?
2. How do you simplify expressions involving powers and roots?
3. Why is the square of a negative number positive?
4. What are the properties of exponents when multiplying or dividing?
5. How can we solve similar problems involving cube roots and exponents?

Tip:

Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) when solving expressions.