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Let's break down the problem to solve it step by step.

### Given:
- 10% of the voters did not cast their vote.
- 10% of the votes cast were invalid.
- The winning candidate got 56% of the valid votes.
- The margin of victory was 1,458 votes.

We need to find the total number of voters enrolled in the voter list.

### Step-by-step solution:

Let the total number of voters enrolled in the list be \( N \).

1. **Voters who cast their vote**: 
   Since 10% did not cast their vote, the remaining 90% of \( N \) cast their votes. So, the number of votes cast is \( 0.9N \).

2. **Invalid votes**: 
   Out of the votes cast, 10% were invalid. Hence, valid votes are 90% of the votes cast, which is \( 0.9 \times 0.9N = 0.81N \).

3. **Votes received by the winning candidate**:
   The winning candidate received 56% of the valid votes. Therefore, the votes received by the winning candidate are:
   \[
   0.56 \times 0.81N = 0.4536N
   \]

4. **Votes received by the losing candidate**:
   Since the margin of victory is 1,458 votes, the losing candidate received:
   \[
   (0.4536N - 1,458) \text{ votes}
   \]

5. **Total valid votes**: 
   The sum of the votes received by the winning and losing candidates should equal the total valid votes:
   \[
   0.4536N + (0.4536N - 1,458) = 0.81N
   \]
   Simplifying this equation:
   \[
   0.9072N - 1,458 = 0.81N
   \]
   \[
   0.0972N = 1,458
   \]
   \[
   N = \frac{1,458}{0.0972} = 15,000
   \]

Thus, the total number of voters enrolled in the voter list is \( \boxed{15,000} \).

Let me know if you need further details or clarifications.

### 5 Related Questions:
1. If the margin of victory was 1,500 votes, how many total voters would be enrolled?
2. What percentage of the total valid votes did the losing candidate receive?
3. How many total votes were cast in this election?
4. If 5% of the total voters had not cast their vote instead of 10%, what would the new total number of voters be?
5. How many invalid votes were there in this election?

### Tip:
When solving percentage-based problems, break the problem into small parts and work systematically to simplify the calculations.

In an election between two candidates, 10% of the voters in the voter list did not cast their vote, whereas 10% of the votes cast were found to be invalid. The winning candidate got 56% of the valid votes and won the election by a margin of 1,458 votes. What is the total number of voters enrolled in the voter list?

Solve the election voting problem where 10% of voters did not cast their vote, 10% of the cast votes were invalid, and the winning candidate got 56% of the valid votes. This problem demonstrates percentage calculation, algebra, and equation solving to find the total number of voters.

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