Is it possible to calculate x-intercept from a mixed model?

I understand that the x-intercept can be calculated using $y = mx + b$ for a linear model. I am unsure if this is statistically appropriate for a mixed model with count data, given that counts cannot be negative and there are random effects to consider. I have seen examples of x-intercept calculations for count data with simple linear regressions, but I'm unsure if this method can be extended to mixed models.

Here is my model:

mod_6 <-  glmmTMB(total_count ~  mean_temp + (1|month) + (1|spread_event),     family = nbinom1, data = dat_nc_ncb)summary(mod_6)

Here is the output.

 Family: nbinom1  ( log )Formula:          total_count ~ mean_ws + (1 | month) + (1 | spread_event)Data: dat_nc_ncb     AIC      BIC   logLik deviance df.resid   1399.1   1415.6   -694.5   1389.1      194 Random effects:Conditional model: Groups       Name        Variance Std.Dev. month        (Intercept) 0.3671   0.6059   spread_event (Intercept) 0.3279   0.5726  Number of obs: 199, groups:  month, 10; spread_event, 26Dispersion parameter for nbinom1 family ():  177 Conditional model:            Estimate Std. Error z value Pr(>|z|)    (Intercept)   3.4928     0.3515   9.936   <2e-16 ***mean_ws      -1.1099     0.5126  -2.165   0.0304 *  ---Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘’ 1

Is it statistically accurate if extract the fixed effects coefficients using coefficients <- fixef(mod_6), identify the coefficient for the intercept using intercept <- coefficients[1], extract the slope using slope <- coefficients[2] and finally extract x-intercept using x_intercept <- -intercept/slope?

Or would be it more appropriate to use a simple glm with quassipoisson family, and then calculate x-intercept. That way, I won't have to worry about random effects?

Details about the experiment

I left out my potted plants in the field for a week, took them back to the glasshouse and counted the number of infected leaves per plant after two weeks. Plants are infected in ideal condition of temperature.

Analysis goal

I need to find lower temperature thresholds. More details can be found in figures 1-4 [here], (http://uspest.org/wea/Boxwood_blight_risk_model_summaryV21.pdf), but the basic idea is that we want to find out temperature at which no disease was observed (lower temperature threshold for disease). Since the goal is to find thresholds, I am happy to let go of the random effects if this allows me to calculate x-intercept for the mean_temp.